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Generalized morrey spaces associated to Schrodinger operators and applications

Authors: 

Nguyen Ngoc Trong, Le Xuan Truong*

Source title: 
Czechoslovak Mathematical Journal, 68(4): 953-986, 2018 (ISI)
Academic year of acceptance: 
2018-2019
Abstract: 

We first introduce new weighted Morrey spaces related to certain non-negative potentials satisfying the reverse Hölder inequality. Then we establish the weighted strong-type and weak-type estimates for the Riesz transforms and fractional integrals associated to Schrödinger operators. As an application, we prove the Calderón-Zygmund estimates for solutions to Schrödinger equation on these new spaces. Our results cover a number of known results.